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    Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model
    <jats:p>In many industries, companies receive customer orders that include multiple products. To simplify the use of optimization models for planning purposes, these orders are broken down, and the quantities of each product are grouped with the same products from other orders to be completed in the same period. Consequently, traditional production planning models enforce minimum demand constraints by product and period rather than by individual orders. An important drawback of this aggregation procedure is that it requires a fixed order fulfillment period, potentially missing opportunities for more efficient resource use through early completion. This paper introduces a novel mathematical formulation that preserves the integrity of customer orders, allowing for early fulfillment when possible. We compare a traditional linear programming model with a new mixed-integer programming approach using a sawmill case study. Although more complex than the traditional model, the proposed formulation reduces costs by approximately 6% by enabling early order completion and offers greater flexibility and control over the production process. This approach leads to better resource utilization and more precise order management, presenting a valuable alternative to conventional production planning models.</jats:p>
    Scopus© Citations 1  50
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    Considering Section Balance in an Integer Optimization Model for the Curriculum-Based Course Timetabling Problem
    (2020) ;
    Patrick Bornhardt
    <jats:p>University course timetabling is a complex and time-consuming duty that every educational institution faces regularly. It consists of scheduling a set of lectures in predefined time slots so as to avoid student conflicts, meet teacher and room availability, and manage several institution-specific operational rules. In this paper, we schedule courses based on a curriculum, that is, before the students’ registration. Unlike other curriculum-based models, the proposed model considers two practical aspects when managing the conflicts between lectures: (i) it schedules sections of subjects so that each section is evenly likely to be registered by the students, and (ii) it considers the failure rates and periodicity a subject is taught. We present a multi-objective integer programming model that maximizes the use of specific time slots, the symmetry in which the lectures of a course are scheduled during a week, and the flexibility for straggler students to take courses. The model is solved using commercial software, and it is applied to a real course-timetabling problem. We show the advantages of its use by comparing the model’s solution with the actual solution obtained by the manual scheduling.</jats:p>
    Scopus© Citations 5  7
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    Scopus© Citations 12  3
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    Towards a Circular Fashion Future: A Textile Revalorization Model Combining Public and Expert Insights from Chile
    (MDPI AG, 2025-09-26) ;
    Priscilla Cabello-Avilez
    The global textile industry has a significant environmental impact, driven by fast fashion and rising consumption, which leads to large amounts of waste. In Chile, this problem is especially visible, with thousands of tons of discarded clothing accumulating in open areas and landfills. This study explores how to design a practical textile revalorization system grounded in local reality. We used a qualitative mixed-methods approach, combining semi-structured interviews with six experts in textile circularity and an online survey completed by 328 people. Thematic analysis revealed low public awareness of textile recycling, limited consumer participation, and major structural barriers, including scarce infrastructure and unclear regulations. Experts emphasized the importance of coordinated action among government, industry, and grassroots recyclers, while survey respondents highlighted the need for education and easier recycling options. Based on these insights, we propose an integrated framework that combines education campaigns, better recycling systems, and formal recognition of informal recyclers’ work. While centered on Chile, the study offers ideas that could support textile circularity efforts in other countries facing similar challenges. By merging expert knowledge with everyday public perspectives, the approach helps design more realistic and socially grounded solutions for textile waste management. As with many exploratory frameworks, external validation remains a necessary step for future research to strengthen its robustness and applicability.
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      14Scopus© Citations 10
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    Scopus© Citations 6  8
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      1
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    Multiperiod Optimisation of Irrigated Crops under Different Conditions of Water Availability
    (2018)
    Mathias Kuschel-Otárola
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    Diego Rivera Salazar
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    Eduardo Holzapfel
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    ;
    We propose a nonlinear optimisation model which maximises profits by resource allocation on a monthly time scale, considering a monthly crop yield model. The proposed model was applied to six management scenarios (two seasonal and four monthly), nine conditions of water availability, and two situations of resource availability under Chilean conditions. These situations provided the same seasonal amount of resources, but different distributions over time. The model included improvements in water resource management such as water storage and water transactions, being the latter a monthly decision variable that can increase farmers’ profits. According to our results, monthly scenarios gave high profits, even better with appropriate resource distribution. When water costs are high, water transactions allow loss reduction of up to 50%. Regarding labour, the lack of availability is more critical than the wages.
      31Scopus© Citations 8
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    Scopus© Citations 20  1
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    Assessing the effectiveness of static heuristics for scheduling lumber orders in the sawmilling production process
    (2024)
    Francisco Vergara
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    ;
    John D. Nelson
    <jats:p>Although optimization models can be used to plan the production process, in most cases static heuristics, such as earliest due date (E), longest processing time (L), and shortest processing time (S), are used because of their simplicity. This study aims to analyze the production cost of the static heuristics and to determine how this cost relates to the size of the production orders in the sawmilling industry. We set a planning problem with different orders and due dates and solved it using two cost-minimization models to compare their solutions. The first was a planning model (PL) where orders were split up into products demand by period, and the second, a planning scheduling (PS) where the sequence of processing orders based on static heuristics was assumed as known. In the latter, the minimum production cost for each static heuristic was found. In both models, the same resource constraints were assumed. The costs showed no significant changes based on order sizes. However, 0,5 % of orders were delayed using PS-E, and 17 % of orders were delayed using PL. PL was an efficient solution method when changing the orders´ size and when looking for the best static heuristic to process the orders. However, PS-E showed the ability to reduce the backlog close to zero while the PL backlog ratio was 17 %. No penalties were applied to backlogs due to their subjective nature; however, when shortages occurred, the demand was unmet or backlogged with substantial costs. Thus, in case the proposed method is adopted using a conservative backlog cost, a sawmill producing under the cut-to-order environment that produces 300000 m3 /year would reduce backlogged orders by 51000 m3. If the holding lumber cost is 2 $/m3, annual savings would be $408000.</jats:p>
      3Scopus© Citations 1